Davis tweeted: "NOLA, I am here to stay! Just getting started" shortly after free agency opened late Tuesday night, and the person confirmed the agreement to The Associated Press on condition of anonymity because the deal cannot yet be signed.
The 22-year-old Davis is entering the final season of a four-year contract he signed after being drafted first overall out of Kentucky in 2012. He had until Oct. 31 to accept the offer or could have become a restricted free agent next offseason.
Davis averaged 24.4 points, 10.2 rebounds and 2.9 blocks this season. The exact value of his extension can't be determined until the salary cap has been set next week.